A two-digit number is 12 more than five times the sum of its digits. The number formed by reversing the digits is 9 less than the original number. The number is:

Correct option is D

Given:

A two-digit number is 12 more than five times the sum of its digits.

The number formed by reversing the digits is 9 less than the original number.

Solution:

10x + y = 5(x + y) + 12 (from the first condition)

10y + x = (10x + y) - 9 (from the second condition)

10x + y = 5(x + y) + 12

10x + y = 5x + 5y + 12

10x - 5x = 5y - y + 12

5x = 4y + 12

5x − 4y = 12_______(Equation 1)

10y + x = 10x + y - 9

10y - y = 10x - x - 9

9y = 9x - 9

Y = x – 1__________(Equation 2)

Putting y = x − 1from Equation 2 into Equation 1

5x - 4(x - 1) = 12

5x - 4x + 4 = 12

x + 4 = 12

x = 8

y = 8 - 1 = 7

Thus, the two-digit number is

10x + y

= 10(8) + 7

= 87.